How to verify the pitch #of nuts?

Functional lot acceptance of thread form can only be effectively assessed with a known good counterpart (GO/NOGO rings or plugs).
That might be a contentious statement, so hear me out.  You can verify components of the helix, (Pitch, Max/Min dia, angles, radii) to verify the threads should work, but until it passes functional gages, you could absolutely have a "good" part fail in the mating part's threads, in the instance mating part is also functionally close to specified limits.

Can you measure pitch with a CMM? YES.  You need to scan (ttp or analog) a line down the axis of the threads.  then you need to define a strategy to quantify the max/min peak/valley's of each thread. Extract the Z height of the peaks/valley's and you've got pitch.   Size of your probe vs pitch is super important here, as well as your machine's ability to probe normal to thread axis.

Sounds very complicated. Thanks for the explanation. 

Sounds very complicated. Thanks for the explanation. 

Verifying thread pitch is pretty simple actually. Most typically use plug/ring gauges that are certified to determine pass/fail. You can use repro rubber for example to make a mold and measure the threads if your requirements call for specific size. Whenever I have a MMC condition on a threaded diameter in the past I use the major or minor diameter to determine the bonus. I have never had an issue in reporting this way. The only issues I have had was trying to report the major/minor diameter size accurately. even with the pitch function it's not easy to hit the peak of the thread especially when you have fine threads.

BigMac said:

Whenever I have a MMC condition on a threaded diameter in the past I use the major or minor diameter to determine the bonus. I have never had an issue in reporting this way.

The problem you would have would be determining the correct bonus because, as you said...

BigMac said:

The only issues I have had was trying to report the major/minor diameter size accurately. even with the pitch function it's not easy to hit the peak of the thread especially when you have fine threads.

If you have not guaranteed that the probe is contacting the crests of the threads, then you cannot be sure you are getting the correct minor/major diameter and therefor the correct bonus calculation.

I've made routines where I run an array of hits along the edge of the threads (as described above), then I parsed out the first Min PR (avoiding lead threads), and aligned Z to that min value.  Voila. As long as pitch is consistent, which you can also extract from that sample array... you will hit along the Min diameter of the threads.

What exactly do you do to parse out your min PR from the array of hits? I've been wondering how other people go about calculating PR, since there isn't an expression command that can pull out PR of a hit.

I am using metric, for pitch 1.5, the distance is 1.5 mm, let us check by every 0.3 mm with diameter 2mm probe,  1-cos( sin-1(0.3)=1-cos(17.5 degree)=0.046 mm.

If check by 0.15mm each( 10 checks), I believe the variation could be below 0.025mm ( This is the MAX, normal should be only half of that). Then pick up the smallest number, adjust the DEPTH.  

Concentricity of threads to -A- - PC-DMIS for CMMs - PC-DMIS - Nexus Community (hexagon.com)

this might help (lazy response i know.  Sorry, i'm super busy this week).